OAM pseudo-doppler receiving architecture

ABSTRACT

The disclosed systems, structures, and methods are directed to an orbital angular momentum (OAM) receiver. The OAM receiver includes at least two receiver antenna elements to receive radiated OAM signal beams containing superposed order modes and to generate antenna element output signals based on the received OAM signal beams. The receiver antenna elements are positioned tangentially along a circular locus and spatially separated by a distance. A variable ratio combining unit operates to switch between the antenna output signals based on a high-rate periodic waveform that emulates unidirectional movement by the antenna elements to produce a pseudo-Doppler frequency shift. The variable ratio combining unit further modulates the antenna output signals based on the periodic waveform to impart a fractional pseudo-Doppler shift to each OAM mode and combines the modulated antenna element output signals in accordance with the fractional pseudo-Doppler shift to facilitate separation of the OAM modes.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to U.S. ProvisionalPatent Application Ser. No. 62/748,226, filed on Oct. 19, 2018 andentitled “OAM Pseudo-Doppler Receiving Architecture”, the contents ofwhich are incorporated herein by reference.

FIELD OF THE INVENTION

The present invention generally relates to the field of radio-frequency(RF) communications, in particular, to systems and methods directed toapplying pseudo-Doppler techniques to substantially enhance theprocessing fidelity and accuracy of received orbital angular momentum(OAM)-based RF communication links.

BACKGROUND

In view of the proliferation of wireless communication usage, numerousproposals have been presented regarding the improvement of servicefacilities for existing wireless communication systems as well as fornext-generation wireless communication systems. Many of the proposedimprovements call for the enhanced capabilities and increasedimplementation of multiple-input, multiple-output (MIMO) andmassive-MIMO (M-MIMO) receiver architectures.

To this end, orbital angular momentum (OAM)-based radio-frequency (RF)signals offer an additional spatial dimension, namely, an additionaldegree of freedom, which can be exploited to enhance the capacity ofwireless communication links.

However, conventional implementations of OAM-based RF communicationshave demonstrated certain deficiencies regarding the effective recoveryof OAM signals at far-field distances.

SUMMARY

An object of the present disclosure is to provide an orbital angularmomentum (OAM) receiver architecture and system. The disclosed systemincludes at least two receiver antenna elements configured to receiveradiated OAM signal beams containing superposed k order modes and togenerate antenna element output signals based on the received OAM signalbeams, in which the receiver antenna elements are positionedtangentially along a circular locus and spatially separated by adistance d. A variable ratio combining unit combines the antenna elementoutput signals in time-varying proportions. The variable ratio combiningunit is configured to switch between portions of the antenna elementoutput signals based on a high-rate periodic waveform of frequency F,the high-rate switching operation emulating unidirectional movement bythe antenna elements to produce a pseudo-Doppler frequency shift. Thevariable ratio combining unit further modulates and time-gates theantenna element output signals based on the high frequency periodicwaveform to impart a fractional pseudo-Doppler shift to each OAM modeand combines the modulated and time-gated antenna element output signalsin accordance with the fractional pseudo-Doppler shift to facilitateseparation of the OAM modes encompassing the streams of information datasymbols.

A further object of the present disclosure is to provide a method forprocessing received orbital angular momentum (OAM) signals. Thedisclosed method includes receiving, by at least two receiver antennaelements, radiated OAM signal beams containing superposed k order modeswherein each of the K modes encompasses an individual stream ofinformation data symbols, in which the receiver antenna elements arepositioned tangentially along a circular locus and spatially separatedby a distance d and a circular locus with a radius R corresponding to afootprint area of the received OAM signal beams, such that the circularlocus contains progressive phase gradient information along acircumference of the circular locus. Antenna element output signals aregenerated based on the received OAM signal beams and are combined by avariable ratio combining unit in time-varying proportions. Portions ofthe antenna element output signals are switched in accordance with ahigh-rate periodic waveform of frequency F, the high-rate switchingoperation providing emulation of unidirectional movement by the receiverantenna elements along the circumference of the circular locus toproduce a pseudo-Doppler frequency shift. The antenna element outputsignals are modulated and time-gated in accordance with the highfrequency periodic waveform to impart a different pseudo-Doppler shiftto each OAM mode. The modulated and time-gated antenna element outputsignals are then combined in accordance with the fractionalpseudo-Doppler shift to facilitate separation of the OAM modesencompassing the streams of information data symbols.

BRIEF DESCRIPTION OF THE FIGURES

The features and advantages of the present disclosure will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIG. 1A (Prior Art) depicts a high-level functional block diagram of aconventional OAM RF generating architecture;

FIG. 1B (Prior Art) depicts a three dimensional graph of representativefar-field OAM RF beam patterns;

FIG. 2A illustrates a conceptual view of a pseudo-Doppler scheme, inaccordance with various embodiments of the present disclosure;

FIG. 2B depicts an interpolated phase between antenna element signalsrepresentative of the pseudo-Doppler effect;

FIG. 2C depicts a representative control waveform configured to switchbetween receiving element signals;

FIG. 3A depicts a high-level functional block diagram of a variableratio power combining unit, in accordance with various embodiments ofthe present disclosure;

FIG. 3B depicts another variable ratio power combining unit thatincorporates a gating unit at the output to emulate unidirectionalantenna element motion, in accordance with various embodiments of thepresent disclosure;

FIG. 4A illustrates a received signal constellation plot for an OAM8beam at a 0 Hz down-conversion frequency shift, in accordance withvarious embodiments of the present disclosure;

FIG. 4B illustrates spectral characteristics for the OAM8 beam at the 0Hz down-conversion frequency shift, in accordance with variousembodiments of the present disclosure;

FIG. 4C illustrates a received signal constellation plot for an OAM1beam at the 0 Hz down-conversion frequency shift, in accordance withvarious embodiments of the present disclosure;

FIG. 4D illustrates spectral characteristics for the OAM1 beam at the 0Hz down-conversion frequency shift, in accordance with variousembodiments of the present disclosure;

FIG. 5A illustrates a received signal constellation plot for an OAM8beam at a 2F down-conversion frequency shift, in accordance with variousembodiments of the present disclosure;

FIG. 5B illustrates spectral characteristics for the OAM8 beam at the 2Fdown-conversion frequency shift, in accordance with various embodimentsof the present disclosure;

FIG. 5C illustrates a received signal constellation plot for an OAM1beam at the 2F down-conversion frequency shift, in accordance withvarious embodiments of the present disclosure;

FIG. 5D illustrates spectral characteristics for the OAM1 beam at the 2Fdown-conversion frequency shift, in accordance with various embodimentsof the present disclosure;

FIG. 6A illustrates a representative spectral envelope and replicas forOAM8, in accordance with various embodiments of the present disclosure;

FIG. 6B illustrates a representative time-limited frequency-shiftstructure for the recovery of OAM modes, in accordance with variousembodiments of the present disclosure;

FIG. 7 illustrates an extended variable ratio power combining unit thatincorporates a gating unit at the output to emulate unidirectionalantenna element motion, in accordance with various embodiments of thepresent disclosure;

FIG. 8A illustrates a high-level functional flow diagram of an OAMsignal recovery process, in accordance with various embodiments of thepresent disclosure; and

FIG. 8B illustrates a detailed functional flow diagram of the OAM signalrecovery process, in accordance with various embodiments of the presentdisclosure.

It is to be understood that throughout the appended drawings andcorresponding descriptions, like features are identified by likereference characters. Furthermore, it is also to be understood that thedrawings and ensuing descriptions are intended for illustrative purposesonly and that such disclosures are not intended to limit the scope ofthe claims.

DETAILED DESCRIPTION

As used herein, the term “about” or “approximately” refers to a +/−10%variation from the nominal value. It is to be understood that such avariation is always included in a given value provided herein, whetheror not it is specifically referred to.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which the described embodiments appertain.

It should be understood that OAM RF waves are configured to manifestvarious orders of OAM modes, denoted by integers ±k. The OAM RF wavesare generated by imposing a phase shift of k2π radians for everyrevolution of the observation point around the beam axis to produce ahelical “corkscrew-shaped” waveform front. This may be achieved by usinga uniform circular array of K identical antenna elements, wherein eachof the K elements is fed by a current that is shifted in phase from thatof its neighboring element in one direction by k2π/K radians at the sameamplitude.

As such, FIG. 1A (Prior Art) illustrates a high-level functional blockdiagram of a conventional OAM RF receiving architecture 100. Asdepicted, OAM architecture 100 comprises a circular array 110 of Kantenna elements a₁-a_(K) and a Butler Matrix structure 120 having Kinput ports C₁-C_(K) and K output ports P₁-P_(K). (For the sake ofsimplicity, K=4 in FIG. 1A). The architecture 100 operates in thereceive mode to sense multiple OAM beam excitations along the circulararray of K antenna elements. This is achieved by coupling the K antennaelements a₁-a_(K) to the K input ports C₁-C_(K) of the Butler Matrixstructure and coupling the K output ports P₁-P_(K) to the K receivers inthe same RF band. Each of the K OAM beams is modulated by a differentstream of independent data symbols, which are fed to a separatereceiver. Being reciprocal, the same structure works in the transmittingmode, with the receivers replaced by transmitters, each of which ismodulated by a different stream of independent data symbols.

FIG. 1B (Prior Art) depicts a three-dimensional graph of representativefar-field OAM RF beam patterns 150. As shown, the OAM beam patternsexhibit a conical shape for all non-zero k orders having “vortex-shaped”axial nulls. The shade gradations indicate the electrical phase at afixed time, modulo-2π radians, in which the phase patterns rotate aroundthe beam axis at the RF rate in time (i.e. one revolution per cycle atRF). In so doing the k phase fronts, as shown by the repeating shadegradations, pass a point on the cone of the k-th OAM beam along thetangential direction, per period of the RF carrier wave. Equivalently,at any given point in time, an electrical phase gradient of k2π/(2πR)radians per meter exists along the circular locus of radius R around theaxis of the conical beam of the k-th order OAM mode.

As noted above, the non-zero k order OAM beam patterns 150 manifest“vortex-shaped” axial nulls at far-field distances, which is typicallywhere conventional receiving antennas/apparatus are positioned.Furthermore, the conventional receiver processing of OAM beams generallyrely on spatial techniques employing the reciprocal principles used togenerate the OAM modes at the transmitter.

As a result, most attempts at exploiting the OAM modes to enhance thecapacity of radio links suffer from low signal-to-noise ratios (SNRs)and acute sensitivity to crosstalk issues due to position errors.Moreover, such attempts impose implementation restrictions on receivingantennas/apparatus, such as requiring the use of large receivingantennas, operational constraints associated with any or all of veryshort wavelengths and limited range distances.

OAM Psuedo-DOPPLER Receiver Scheme and System Architecture

The present disclosure provides an OAM RF receiver scheme andarchitecture that implements a pseudo-Doppler technique. The OAMpseudo-Doppler architecture refers receiver systems, devices, and otherstructures embodying the pseudo-Doppler technique. This techniqueprovides a frequency domain-based solution to obviate or mitigate theabove-noted limitations of conventional receiver schemes. As will bedescribed in greater detail below, the disclosed embodiments provide fora pseudo-Doppler scheme that operates to enable toggling or gradualswitching between signals outputted by at least two fixed,spatially-separated receiving antenna elements to artificially emulate aunidirectional antenna movement commensurate with traditionalDoppler-based processing.

The emulated antenna movement is achieved by a rapid, periodic,modulating waveform controlling a variable ratio RF power combining(VRPC) unit that drives the toggling between the signals outputted bythe antenna elements within defined time intervals. The VRPC unitsubsequently combines the modulated antenna element signals andtime-gates those signals for further processing designed to separate anddemodulate the received OAM beams into meaningful payload data.

OAM Psuedo-DOPPLER Scheme

In traditional Doppler-based RF direction-finding applications,physically moving antennas are used to resolve angular direction basedon detected frequency shifts of the received signal. By way of briefsummary, such Doppler-based applications employ antenna element(s) thatphysically move (i.e., rotate) along a circular locus at a constanttangential velocity. The tangential velocity imparts a proportionalDoppler frequency shift, which is imposed on the signal received at theantenna element(s) to frequency modulate (FM) the received signal. TheFM signal manifests a deviation equivalent to the frequency shift and aphase corresponding to the azimuthal direction of the arriving receivedsignal. The azimuthal angular direction is then resolved as a functionof the FM phase information.

With this said, the disclosed embodiments present a scheme that exploitsthe principles noted above to artificially emulate the physical rotatingmotion of the antenna element(s) and create a pseudo-Doppler effectbased on the phase gradient of an on-axis OAM beam. The pseudo-Dopplereffect imparts a Doppler frequency shift that is proportional to theorder k of each of the OAM modes of the received signals, therebyfacilitating mode separation processing and subsequent extraction ofpayload data.

In particular, FIG. 2A illustrates a conceptual view of pseudo-Dopplerscheme 200, in accordance with various embodiments of the presentdisclosure. The depicted annular circular ring represents the footprintarea of a k-th order OAM received conical beam, in which the shadegradations indicate spatial phase progression, or gradient, at a giventime instant along the circular locus of the footprint annular ringdefined by radius R. As shown, scheme 200 employs two receiver antennaelements RX1, RX2 that are fixedly positioned tangentially to thecircular locus and are spatially separated by a distance d. With thisarrangement, the physical movement of traveling along the circular locusmay be artificially emulated by gradually switching between antennaelements RX1, RX2, in one direction, repeatedly.

That is, as shown in FIG. 2A, antenna elements RX1, RX2 are fixedlypositioned along the circular locus separated by distance d. However, byrapidly and periodically toggling between portions of the signaloutputted by elements RX1, RX2 over time, the appearance ofunidirectional circumferential movement is achieved. The emulatedcircumferential movement is indicated by the interpolated elementpositions and the shaded arrow depicted in FIG. 2A. So, as the emulatedmovement appears to travel from one interpolated position to another,the corresponding changes in phase incurred by the emulated movementalong the phase gradient produces a pseudo-Doppler frequency shifteffect.

FIG. 2B depicts a representative virtual antenna phase u(t) effected bya control waveform P(t) configured to drive the rapid, periodicswitching between the signals outputted by antenna elements RX1, RX2. Asshown, control waveform P(t) manifests a “saw-tooth” or unidirectionalprofile that rapidly and periodically toggles between the elements RX1,RX2 signals having respective phases φ₁ and φ₂.

It will be appreciated that the principles and concepts presented by theinstant disclosure are not limited to the use of the control waveformP(t) noted above and implied by FIG. 2B, as other suitable waveformscapable of rapid, unidirectional, and periodic switching may be used.For example, FIG. 2C provides an alternative control waveform P_(s)(t).P_(s)(t) comprises orthogonal sinusoidal waveforms in which a sinemodulation is applied to one antenna element output signal and a cosinemodulation is applied to the other antenna element output signal, withsuitable time-gating to emulate directionality in the final outputsignal, as in the embodiment depicted in FIG. 3B.

With regard to the time-gating functionality, it will be noted that thenecessity of such functionality is a consequence of the limits of theregion of validity relative to the pseudo-Doppler frequency shift whenusing the sine and cosine control waveforms where P(t)=Ωt. The regionallimits of validity are periodic, the fundamental period in terms ofphase being:

$\begin{matrix}{\frac{- \pi}{2} < {\Omega\; t} < 0} & (1)\end{matrix}$which repeats at intervals of ±nπ as shown in FIG. 2C. Thus, thetime-gating should occur periodically in real time to ensure the desiredfrequency shifts in the final output and should be synchronous with thepseudo-Doppler modulation.

It follows that the gating intervals are designed to contain thoseportions of the modulations which cause one antenna output to beincreasing and the other decreasing the magnitude of its contribution tothe final output signal. As shown in FIG. 2C, the alternating signs ofthe gating waveform ensure that always the same antenna output isincreasing while the other is decreasing. In so doing, pseudo-Dopplerscheme 200, performs the desired interpolation that emulates aunidirectionally moving antenna between the two stationary receiveantennas.

OAM Pseudo-DOPPLER System Architecture

As depicted in FIG. 2A and noted in the description of pseudo-Dopplerscheme 200, the signals outputted by antenna elements RX1, RX2 aresupplied to a variable ratio power combining (VRPC) unit 300. VRPC unit300 is configured to drive the switching between the signals outputtedby elements RX1, RX2 to emulate unidirectional antenna movement based ona rapid, periodic, control waveform as well as combine the outputtedsignals. This emulated movement must be sufficiently rapid to effect apseudo-Doppler shift that is at least as large as the bandwidth of eachOAM mode modulation signal, so the OAM mode signals can be separated infrequency. This movement typically far exceeds any physically-realizableactual movement of the RX antenna elements.

In view of scheme 200 described above, it will be appreciated that thereference phase (relative to a fixed reference position on thefootprint) for the emulated moving antenna element between RX1, RX2 maybe expressed as:φ_(n) =kθ _(n)  (2)

where k is the OAM mode order and θ_(n) is the azimuthal angularposition of the receiver element. It follows that, as antenna elementsRX1, RX2 emulate movement of one antenna around the circular locus at auniform velocity v, its emulated angular position changes linearly withtime, thereby causing corresponding phase value changes in its outputthat also vary linearly with time. The time-based phase variances may beexpressed as:

$\begin{matrix}{\frac{d\;\varphi_{n}}{d\; t} = {\frac{k\; d\;\theta_{n}}{d\; t} = {\frac{k\; v_{n}}{R} = {2\;\pi\; f_{n,{Doppler}}}}}} & (3)\end{matrix}$

$\begin{matrix}{{{in}\mspace{20mu}{which}\mspace{14mu} v_{n}} = {{\frac{d}{d\; t}( {R\;\theta_{n}} )\mspace{14mu}{and}\mspace{14mu} 2\;\pi\; f_{n,{Doppler}}} = \frac{k\; d\;\theta_{n}}{d\; t}}} & (4)\end{matrix}$where R is the radius of the circular footprint locus. Thus, thespatial-domain properties of the OAM k-order beams include phasegradient information k/R which, by virtue of the emulated motion ofantenna elements RX1, RX2, may be transformed to frequency-domaincharacteristics, namely, transverse Doppler shift f_(n, Doppler). Itwill be noted that Doppler shift f_(n, Doppler) is directly proportionalto the received OAM mode k while remaining independent of the RF carrierfrequency. It will be appreciated that the disclosed embodiments aim toreplicate such a Doppler shift by replacing the role of the antennavelocity v with a toggling action between two separate but fixedantennas at a rate proportional to F, which is designated as thepseudo-Doppler frequency.

Given this context, the phases of the RF waves embodied by the OAM modek beams received by antenna elements RX1, RX2 referenced as ψ₁, ψ₂advance at k multiples of 2π radians for one complete cyclical triparound the circular footprint 2πR, at any given point in time. As such,the phases ψ₁, ψ₂ differ by kd/(2πR) for a portion of the footprintcovered by the antenna element separation d. Therefore, the relationshipbetween the respective phases ψ₁, ψ₂ of receiver antenna elements RX1,RX2 at time t may be expressed as:

$\begin{matrix}{{\psi_{2}(t)} = {{\psi_{1}(t)} - {k\; 2\;{\pi( \frac{d}{2\;\pi\; R} )}}}} & (5)\end{matrix}$with the relationship between phases ψ₁, ψ₂, the inputs to VRPC unit300, referenced as W₁, W₂, may be modeled, as follows:W _(1,k)(t)=S _(k)(t)e ^(jψ) ¹ ^((t))W _(2,k)(t)=S _(k)(t)e ^(jψ) ² ^((t)) =S _(k)(t)e ^(jψ) ¹^((t)−jkd/R)  (6)where S_(k)(t) is the signal of the k-th OAM beam received at thereference point in the far field. Furthermore, when P(t)=Ωt, Ω=2πF isthe radian pseudo-Doppler frequency, F is the corresponding frequency inHz, and the far-field condition kd/(2R)<<π/4 is met, one of the twooutputs of VRPC unit 300, referenced as Z_(l, k)(t), may be approximatedat selected gating time intervals by:

${Z_{1,k}(t)} \approx {\sqrt{2}{S_{k}(t)}\;{e^{j(\;{{\psi_{1}{(t)}} - \frac{k\; d}{2\; R}})}( {\cos( {{\Omega\; t} + {\pi/4}} )} )}e^{{j{(\frac{k\; d}{2R})}}{({{\Omega\; t} + {\pi/4}})}}}$

Armed with these relationships, the implementation of VRPC unit 300 maybe realized. To this end, FIG. 3A illustrates a high-level functionalblock diagram of VRPC unit 300, in accordance with various embodimentsof the present disclosure. In the illustrated embodiment, VRPC unit 300incorporates two hybrid combiners 310, 316 and two oppositely-adjustedvariable phase shifters 312, 314. The variable phase shifters 312, 314are modulated by the control waveform P(t), as noted above, at a veryhigh rate proportional to F. The output may then be expressed as:

$\begin{matrix}{{Z_{1,k}(t)} = {{S_{k}(t)}\;{e^{j\;{\psi_{1}{(t)}}}\lbrack {{\cos( {P(t)} )} - {e^{\frac{{- j}\; k\; d}{R}}{\sin( {P(t)} )}}} \rbrack}}} & (8)\end{matrix}$where the k-th OAM mode signal may be modeled as the product of adata-modulation envelope and an RF carrier phasor:S _(k)(t)=m _(k)(t)e ^(jωt)  (9)

As shown in FIG. 3A, the outputs of receiving antenna elements RX1, RX2are coupled to input ports W₁ and W₂ of VRPC unit 300, respectively, andthe output is taken at port Z₁. It will be understood that at least oneof port Z₂ and a switching arrangement between ports port Z₁, Z₂ to acommon output port could also be used, consistent with the principles ofthe instant disclosure pertaining to subsequent time-gating arrangementsto effect unidirectionality in the pseudo-Doppler frequency shifts.

The periodic waveform P(t) is applied to a control port and operates thevariable phase-shifters in opposing directions at a high rateproportional to F. In so doing, the Z₁/Z₂ output signal will appear tobe shifted by a fraction of the pseudo-Doppler frequency, Fkd/(2R),which functionally corresponds to the originally desiredtransverse-Doppler shift, f_(n,Doppler) as represented by equation (4).

In this manner, VRPC unit 300 is capable of combining the outputs ofantenna elements RX1, RX2 in time-varying proportions ranging from onlyRX1 output, to half of each of the RX1, RX2 outputs, to only RX2 output.This is, in effect a form of gradual switching between the antennaelements in one direction that should be repeated periodically at somerate.

FIG. 3B illustrates a high-level functional block diagram of analternative VRPC unit 350, in accordance with various embodiments of thepresent disclosure. In the illustrated embodiment, VRPC unit 350comprises two multipliers 352, 354, a hybrid combiner 356, and aswitching and time-gating unit 358, 360. In this embodiment, the outputsof antenna elements RX1, RX2 are supplied to multipliers 352, 354. VRPCunit 350 is mathematically equivalent to VRPC unit 300, but effectivelyuses P(t)=Ωt, where Ω=2πF to apply quadrature sinusoidal waveforms atthe pseudo-Doppler frequency F to the inputs of each of multipliers 352,354.

The multiplier 352, 354 outputs are subsequently combined by hybridcombiner 356 to yield output signals Z₁, Z₂. The switching andtime-gating unit 358, 360 operates to provide a synchronous time-gatingfunction to limit the two output signals Z₁, Z₂ to the time-intervals ofvalidity when the desired fractional pseudo-Doppler frequency shiftoccurs Thus, much like the embodiment of VRPC unit 300, VRPC unit 350yields output signal Z₁/Z₂ that appears to be shifted by a fraction ofthe pseudo-Doppler frequency, Fkd/(2R), which functionally correspondsto the originally desired transverse-Doppler shift, f_(n,Doppler).

OAM Pseudo-DOPPLER Simulation Results

Simulation trials were conducted based on the OAM pseudo-Doppler systemarchitectures disclosed above. After modulation by the pseudo-Dopplerwaveforms, time-gating and down-conversion operations, the constellationand spectrum of the composite received signal are illustrated. Theconstellations pertain to the spectral replica centered at baseband (0Hz frequency) in the spectral plots after the frequency shifting by thedown-converter, reflecting a low-pass filtering operation performed inthe simulation prior to demodulation. For simplicity of illustration,only one frequency-shift operation is performed in the down-converter,as opposed to the full structure of the OAM recovery scheme illustratedlater in FIG. 6B.

FIGS. 4A, 4B depict the constellation plot and spectral characteristicsof OAM mode 8 (OAM8) at a 0 Hz frequency shift in the down-converter, inaccordance with various aspects of the present disclosure. Similarly,FIGS. 4C, 4D depict the 64 QAM constellation plot and spectralcharacteristics of OAM mode 1 (OAM1) at the 0 Hz frequency shift in thedown-converter, in accordance with various aspects of the presentdisclosure.

The resulting spectral replicas of each of two simulated modes OAM8 andOAM1 that are transmitted and received separately are depicted by FIGS.4B, 4D, respectively. The complex 64 QAM constellations are depicted byFIGS. 4A, 4C, respectively. It is apparent that each OAM mode has adifferent spectral envelope and that the baseband (centered at 0 Hz)spectral replica contains a different proportion of each OAM mode, asevidenced by the relative sizes of their constellations andcorresponding baseband spectra.

Therefore, at a frequency shift of 0 Hz in the down-converter, OAM8 issuperior to OAM1. With suitable scaling by a complex coefficient (i.e.,amplitude and phase change), OAM8 could be recovered even in thepresence of OAM1, and after suitable conventional equalization anddecoding, its QAM data symbols may be successfully demodulated.

With a different frequency shift applied at the down-converter,different proportions of each OAM mode may be achieved and allow for therecovery of other OAM modes. Thus, FIGS. 5A, 5B depict the constellationplot and spectral characteristics of OAM8 at a 2F (i.e., twice thepseudo-Doppler modulation frequency) frequency shift in thedown-converter, in accordance with various aspects of the presentdisclosure. Similarly, FIGS. 5C, 5D depict the constellation plot andspectral characteristics of OAM1 at the 2F frequency shift in thedown-converter, in accordance with various aspects of the presentdisclosure.

As demonstrated by FIGS. 5A-5D, the OAM proportions of OAM8 and OAM1 areroughly the inverse of those shown in FIGS. 4A-4D. That is, at afrequency shift of 2F in the down-converter, OAM1 is superior to OAM8,so OAM1 could be similarly recovered and demodulated in the presence ofOAM8.

Without any other signal processing, each OAM mode was recovered fromthe composite signal with a bit error rate (BER) on the order of ≈10⁻¹.In general, the differences in relative proportions of OAM modes in thevarious spectral replica will not be as conveniently large asillustrated in simulated trials and they will need to be recovered fromseveral spectral replicas by jointly inverting their proportions using amatrix-vector multiplication scheme, as illustrated later in FIG. 6B.Moreover, the expected spectral shifts by fractions of thepseudo-Doppler modulation frequency appear to be absent in all of theoutput spectral replicas, but they are actually present in theirenvelopes, as will be indicated by FIG. 6A.

OAM Pseudo-DOPPLER Recovery Scheme

Based on the simulation trials, the OAM signals are present in differentproportions in the various harmonic spectral replicas of the compositereceived signal at the output of the gating subsystem of the OAM systemarchitecture noted above. These proportions are determined by thephysical parameters of the link, which can be made known to the receivera-priori, to enable effective recovery of the OAM modes.

Moreover, the gating pseudo-Doppler modulations of the compositereceived signal evidence a “time-limited fractional frequency shift”operation in the discrete frequency domain. This may be recognized asthe dual of a “frequency-limited fractional time shift”, or band-limitedfractional delay operation on a signal in discrete time domain. That is,the gating frequency, which is twice the pseudo-Doppler modulationfrequency 2F and the fraction comprising the OAM spectral shift, Fkd/(2R), correspond to the sampling interval and the fraction thereof,respectively, in the band-limited fractional-delay operation.

The correspondence to the sampling interval and the fraction thereof maybe expected based on the duality relations that exist between time andfrequency domains due to properties of the Fourier transform and itsinverse. The property that sampling in the time-domain at intervals of Tcauses periodic extensions in frequency-domain by 1/T, also explains thereceived spectra observed in the simulation trials. The samplingoperation is analogous to the time-gating functionality according toequation (1) and as depicted in FIG. 2C.

Moreover, as discussed above regarding the simulation results of OAM8and OAM1 and depicted by FIGS. 4A-4D and 5A-5D, each OAM mode has adifferent spectral envelope and the corresponding spectral replicascontain different proportions of each OAM mode, as evidenced by therelative sizes of their constellations. The proportions of OAM modes inthe spectral replicas are determined by the spectral envelopes and eachOAM mode's spectral envelope exhibits its characteristic fractionalpseudo-Doppler shift.

These characteristic fractional shifts may be determined frominformation known at the receiver. For example, FIG. 6A illustrates arepresentative spectral envelope and replicas for OAM8, in which thefractional shift in the envelope is identified by the dashed verticalline and the spectral replicas are indexed by values of m.

FIG. 6B depicts a representative time-limited frequency-shift structure600 for the recovery of OAM modes, in accordance with various aspects ofthe present disclosure. Structure 600 provides an exemplary model forrecovering a desired OAM mode from the superposition of all OAM modesthat appear at the gating output of the pseudo-Doppler modulationsubsystem.

As depicted, the gating output is passed through a series ofdown-converters that perform frequency-shifts at multiples of 2F tobaseband and the resulting M low-pass filtered baseband components arerepresented in vector X. It will be appreciated that, whilefrequency-shifts at multiples of 2F is disclosed, it is not intended tobe limiting, as frequency-shifts at other multiples of F may be suitablyemployed.

The k-th row of coefficients {C_(k,m)} may then be used to recover thek-th order OAM mode from X, as the k-th entry of vector Y. Moreover, theentire broad-band spectrum of the gating output will contain spectralreplicas of the transmitted signals located at the M harmonics of thepseudo-Doppler modulation frequency 2F. Further, it will be noted thatthe input and output signals of structure 600 are in the continuous-timedomain and may also be in analog form.

In view of the above, the spectrum of each k-th order OAM mode at thegating output may be expressed as:

$\begin{matrix}{{Z_{G,k,1}(f)} = {{U_{k,{C\; S}}(f)}{\sum\limits_{m = {- \infty}}^{\infty}{S_{k}( {f - {m\; 2\; F}} )}}}} & (10)\end{matrix}$

-   -   where U represents the spectral envelope.

The values of U_(k) at spectral replica positions m can be arranged in avector U of length M, and K such vectors determined for the K incidentOAM modes. These may then be arranged column-wise in an M×K matrix U,and the input vector X_(M×1) to each of the K down-convertingcoefficient branches may be expressed jointly as:X _(M×1) =U _(M×K) S _(K×K) A _(K×1)  (11)

-   -   where M≥K

Given these relationships, the incident OAM modes may be recovered byemploying a pseudo-inverse of matrix U, as defined by:U _(K×M) ^(#)=[U _(K×M) ^(H) U _(M×K)]⁻¹ U _(K×M) ^(H)  (12)which is equal to matrix C, containing the baseband weightingcoefficients {C_(k,m)} in FIG. 6B.

It then follows that a vector Y_(K×1) of output OAM modes of length Kmay be obtained by:Y _(K×1) =U _(K×M) ^(#) X _(M×1) =S _(K×K) A _(K×1)  (13)

This is because each envelope vector comprising the columns of matrix Uis generally linearly independent of K−1 of the other vectors and thegreater M is (i.e. the more spectral replicas are included in matrix U),the higher is the likelihood of that being the case.

The entries of output vector Y_(K×1) may then be subsequently processedand equalized as in a conventional digital (i.e., QAM) receiver anddemodulated into data streams. The demodulated data streams may then berecombined to form the final data output.

With this said, FIG. 8A depicts a high-level functional flow diagram ofOAM signal recovery process 800, in accordance with various embodimentsof the present disclosure. As shown, process 800 begins at task block802, in which mode k OAM beam signals manifesting different data streamsper each mode k are received by at least two antenna elements. The atleast two antenna elements are separated by distance d along a circularlocus having a radius R corresponding to the footprint area of thereceived OAM beams and operate to output antenna element signals inresponse to the received OAM beam signals.

At task block 804, the outputted antenna element signals are processedand combined by a variable ratio combining unit, in accordance with ahigh-rate periodic waveform having a frequency F that is greater than2BR/d, where B is the common bandwidth occupied by the transmitted andreceived OAM beam signals. The high-rate periodic waveform operates tocontrol the rapid switching between portions of the outputted antennaelement signals to emulate unidirectional movement by a virtual,interpolated receiver antenna element along the circumference of thecircular locus. The emulated receiver antenna element movement producesa fractional pseudo-Doppler frequency shift that results from itspassage through the characteristic phase gradient of each OAM beamfootprint along the circular locus.

The high-rate periodic waveform also serves to modulate and time-gatethe outputted antenna signals so as to limit them to the time-intervalsduring which fractional pseudo-Doppler shift imparted to each of thereceived OAM modes is valid and unidirectional. In so doing, thevariable ratio combining unit operates to proportionally combine themodulated, time-gated antenna element output signals to form a broadbandoutput signal at its output ports Z₁, Z₂.

At task block 806, the combined modulated, time-gated antenna elementoutput signals are shifted by multiples of frequency F and then low-passfiltered to generate baseband signals X_(m). At task block 808, thebaseband signals X_(m) are each multiplied by a weighting coefficientC_(k,m) and then summed up to provide separate k-th OAM mode basebandsignals Y_(k). And, at task 810, process 800 operates to apply samebaseband signal vector X to all K rows of the complex-valued weightingcoefficients in order to collect all OAM mode outputs in output vectorY.

At task block 812, process 800 operates to equalize and demodulate eachof the K OAM mode signals Y_(k) and at task block 814, recombine the Kdemodulated data streams.

FIG. 8B depicts a comprehensive detailed functional flow diagram of theOAM signal recovery process 850, in accordance with another embodimentof the present disclosure. As shown, process 850 begins at task block852, in which at least two suitably-disposed antennas simultaneouslyreceives an RF signal composed of OAM beams modulated by separate datastreams that are superposed in space and carrier frequency. At taskblock 854, the received antenna signals are coherently converted tobaseband or a suitable intermediate frequency IF (a 0 Hz carrier isassumed). The converted baseband antenna signals are also simultaneouslyforwarded to task 857 for operations during training or calibrationmodes.

At task 856, the converted baseband antenna signals are modulated suchthat the amplitude of one signal is uniformly increasing while theamplitude of the other signal is commensurately decreasing duringrepeated time intervals at a rate F. At task 858, the modulated antennasignals are combined and may be gated in accordance with theabove-designated time intervals synchronously with modulation rate F.Then at task 860, the combined timed-gated signals are shifted bymultiples of F and then low-pass filtered to baseband.

As noted above, the converted baseband antenna signals aresimultaneously forwarded to task 857 in which, duringtraining/calibration operations, one of the converted baseband antennasignals is delayed by the delay of a variable-ratio power combiner(VRPC). At task 859, the VRPC-delayed baseband signal is subsequentlycorrelated with the shifted baseband signals produced by task 860 and,in task 861, updated calibration coefficients C_(k,m) are obtained fromthe correlation results.

At task 862, the shifted baseband signals produced by task 860 arearranged in a row vector X, multiplied by the updated calibrationcoefficients C_(k,m) produced by task 861, and then summed to obtain aseparated k-th OAM mode baseband signal. In task 864, the same basebandsignal vector operation is applied to all K rows of weightingcoefficients and the K OAM mode baseband signals are collected in outputvector Y.

At task 866, each of the K OAM mode baseband signals are equalized anddemodulated and, at task 868, the K OAM mode baseband signals arerecombined.

Extended OAM Pseudo-DOPPLER System Architecture

FIG. 7 depicts an extended VRPC unit 700 that also incorporates a gatingunit at the output to emulate unidirectional antenna element motion, inaccordance with various embodiments of the present disclosure. ExtendedVRPC unit 700 builds on the principles noted above to achieve greatersensitivity of the fractional pseudo-Doppler effect by incorporatingmultiple two-element pseudo-Doppler modulation subsystems to servicemore than two antenna elements.

In the illustrated embodiment, extended VRPC unit 700 is configured toservice four antenna elements, RX1, RX2, RX3, RX4 by employing twofirst-stage two-element pseudo-Doppler modulation subsystems 702, 704,and a final-stage two-element pseudo-Doppler modulation subsystem 706.As shown, each of the modulation subsystems 702, 704, 706 embody theconfiguration of alternative VRPC unit 350 in which all of subsystems702, 704, 706 are modulated synchronously with the same phase by thesame source of Ω=2πF. The two first-stage subsystems 702, 704 eachoperate to process two of the outputted antenna element signals,respectively, and the outputs of the first-stage subsystems 702, 704 aresubsequently fed to final-stage modulation subsystem 706.

By virtue of the system architecture of extended VRPC unit 700 that isconfigured to service additional antenna elements, the signal amplitudesof the additional elements may combine coherently while noise maycombine incoherently to yield improved SNR. Moreover, incorporating asecond output may be useful in providing at least one of some diversityin the OAM recovery process and the use of multipath signals.

It will be noted that, if the two first-stage modulation subsystems 702,704 were again separated by “d”, the differences in their phases wouldappear in their ψ₁(t) phase terms and result in a double fractionalpseudo-Doppler shift at the output of final-stage modulation subsystem706 whose inputs they provide. This is because the separation of theirrespective antenna elements would to be 2d. Theoretically that would addto the first-stage systems 702, 704 shifts to triple the fractionalpseudo-Doppler frequency shift at the final second-stage output. Theprocess could then be iterated for more elements and more stages of theoriginal subsystem.

However, by just moving the original two antenna elements of onesubsystem from d to the same total span of 3d would effectively achievethe same result, so there would be no net gain in doing so. Therefore,sub-dividing the separations to d/3 could conceivably improve the SNRwith the same net fractional pseudo-Doppler shift. That could allowoperation closer to the OAM beam axis where SNR is lower, but because Rwould also be lower, the net fractional pseudo-Doppler shift would beincreased.

Moreover, by coinciding the gating intervals for Z₁, Z₂, makes theirfractional pseudo-Doppler shifts opposite in sign within the same spand, so the resulting difference would be twice the size of the shift atone output. That may be exploited to enhance the separability ofclosely-spaced OAM modes or in their recovered SNR, or in separatingmultipath components which will have negative corresponding OAM ordersfor odd number of reflections.

OAM Psuedo-DOPPLER Receiver Scheme and System Architecture Advantages

By virtue of the disclosed embodiments, the described receiver systemarchitecture and scheme avoids the need to have large, complex receivingantenna structures designed to capture the entire circumferential phaseprogressions of the OAM beam signals. Moreover, the disclosed systemarchitecture and scheme overcomes the susceptibility to low SNR as wellas the limitation in range distances, and the need to precisely alignthe TX and RX antenna structures. It also affords a K×K MIMOfunctionality without requiring K antennas at the receiver, as only 2antennas are required to recover any number K of OAM mode signals withthis inventive scheme.

In view of these attributes and capabilities, the described receiversystem architecture and scheme may be advantageously integrated intoexisting and future MIMO and massive-MIMO receiver infrastructures.

What is claimed is:
 1. An orbital angular momentum (OAM) receiversystem, comprising: at least two receiver antenna elements configured toreceive radiated OAM signal beams and generate antenna element outputsignals based on the received radiated OAM signal beams, the receiverantenna elements positioned tangentially along a circular locus andspatially separated by a distance d; the radiated OAM signal beamscontaining superposed order modes in which each of the order modes isdenoted by integer k and a total number of superposed modes is denotedby integer K, wherein each of the K modes encompasses an individualstream of information data symbols; the circular locus having a radius Rcorresponding to a footprint area of the received radiated OAM signalbeams, wherein the circular locus contains a characteristic phasegradient pertaining to each OAM beam along a circumference of thecircular locus; and a variable ratio combining unit operative to receiveand combine the antenna element output signals in time-varyingproportions, the variable ratio combining unit configured to: switchbetween portions of the antenna element output signals in accordancewith a high-rate periodic waveform of frequency F, the high-rate switchoperation providing emulation of unidirectional movement by a virtualreceiver antenna element along the circumference of the circular locusto produce a pseudo-Doppler frequency shift; modulate and time-gate theantenna element output signals in accordance with the high-rate periodicwaveform to impart a fractional pseudo-Doppler shift to each OAM mode;and combine the modulated and time-gated antenna element output signalsin accordance with the fractional pseudo-Doppler shift to facilitateseparation of the OAM modes encompassing streams of information datasymbols.
 2. The OAM receiver system of claim 1, wherein the frequency Fof the high-rate periodic waveform satisfies a relationship: F>2BR/d,where B is a bandwidth of the received OAM signals.
 3. The OAM receiversystem of claim 1, wherein the variable ratio combining unit comprisesoppositely-adjusted variable phase shifting elements that are modulatedby the high-rate periodic waveform.
 4. The OAM receiver system of claim1, wherein the variable ratio combining unit comprises multiplyingelements that are modulated by the high-rate periodic waveform.
 5. TheOAM receiver system of claim 4, wherein the variable ratio combiningunit comprises a synchronous time-gating unit that is controlled by thehigh-rate periodic waveform.
 6. The OAM receiver system of claim 1,wherein the variable ratio combining unit comprises at least one hybridcoupling element.
 7. The OAM receiver system of claim 1, wherein themodulated, time-gated antenna element output signals are shifted bymultiples of frequency F then low-pass filtered to generate basebandsignals.
 8. The OAM receiver system of claim 7, wherein the basebandsignals are each multiplied by a weighting coefficient and then summedup to provide separate k-th OAM mode baseband signals.
 9. The OAMreceiver system of claim 1, further comprising four antenna elements,two first-stage variable ratio combining units, and a final stagevariable ratio combining unit wherein separation of the antenna elementscorresponding to the two first stage variable ratio combining units is2d.
 10. The OAM receiver system of claim 9, wherein the two first-stagevariable ratio combining units and the final stage variable ratiocombining unit are modulated synchronously with a same phase by thehigh-rate periodic waveform.
 11. A method for processing orbital angularmomentum (OAM) signals, comprising: receiving, by at least two receiverantenna elements, radiated OAM signal beams containing superposed ordermodes in which each of the order modes is denoted by integer k and thetotal number of superposed modes is denoted by integer K, wherein eachof the K modes encompasses an individual stream of information datasymbols, the receiver antenna elements being positioned tangentiallyalong a circular locus and spatially separated by a distance d, thecircular locus having a radius R corresponding to a footprint area ofthe received radiated OAM signal beams wherein the circular locuscontains progressive phase gradient information along a circumference ofthe circular locus; generating, by the receiver antenna elements,antenna element output signals based on the received radiated OAM signalbeams; combining, by a variable ratio combining unit, the antennaelement output signals in time-varying proportions; switching betweenportions of the antenna element output signals in accordance with ahigh-rate periodic waveform of frequency F, the high-rate switchingoperation providing emulation of unidirectional movement by the receiverantenna elements along the circumference of the circular locus toproduce a pseudo-Doppler frequency shift; modulating and time-gating theantenna element output signals in accordance with the high-rate periodicwaveform to impart a fractional pseudo-Doppler shift to each OAM mode;and combining the modulated and time-gated antenna element outputsignals in accordance with the fractional pseudo-Doppler shift tofacilitate separation of the OAM modes encompassing streams ofinformation data symbols.
 12. The method of claim 11, wherein thefrequency F of the high-rate periodic waveform satisfies a relationship:F>2BR/d, where B is a bandwidth of the received OAM signals.
 13. Themethod of claim 11, wherein the variable ratio combining unit comprisesoppositely-adjusted variable phase shifting elements that are modulatedby the high-rate periodic waveform.
 14. The method of claim 11, whereinthe variable ratio combining unit comprises multiplying elements thatare modulated by the high-rate periodic waveform.
 15. The method ofclaim 14, wherein the variable ratio combining unit comprises asynchronous time-gating unit that is controlled by the high-rateperiodic waveform.
 16. The method of claim 11, wherein the variableratio combining unit comprises at least one hybrid coupling element. 17.The method of claim 11, further comprising shifting the modulated,time-gated antenna element output signals by multiples of frequency Fand low-pass filtering the antenna element output signals to generatebaseband signals.
 18. The method of claim 17, further comprisingmultiplying the baseband signals by a weighting coefficient and summingup to provide separate k-th OAM mode baseband signals.
 19. The method ofclaim 11, further comprising providing four antenna elements, twofirst-stage variable ratio combining units, and a final stage variableratio combining unit wherein the separation of the antenna elementscorresponding to the two first stage variable ratio combining units is2d.
 20. The method of claim 19, further comprising modulating the twofirst-stage variable ratio combining units and the final stage variableratio combining unit synchronously with a same phase by the high-rateperiodic waveform.